It sort-of does work with people's existing email (since the public key is just added as an email alias). If you didn't have the public key in the email, you'd have to have central repo for public keys, which is what this technique is trying to prevent.
Also, this is an unhosted application, so you can just right click and save-as. It still works hosted on your local filesystem (which isn't subject to NSLs).
Indeed. Unfortunately, that's fundamentally the way public-key crypto works. If you do try to send a message to an email with no public key, it will prompt you to send an invite instead.
Gmail[1], Outlook[2], and Yahoo[3] supposedly support aliases, and everyone who uses Google Apps for their email also support aliases. I've only verified with my Gmail, so can anyone else confirm Outlook and Yahoo?
Also, this is an unhosted application, so you can just right click and save-as. It still works hosted on your local filesystem (which isn't subject to NSLs).